In this study, a two-dimensional, three-velocity particle-in-cell/Monte Carlo collision model is employed to systematically investigate the beam transport of high-energy negative ion beams in a gas target neutralization chamber. Owing to the high charge density of high-energy negative ion beams, the space-charge-induced electrostatic repulsion induces pronounced beam divergence during transport. Under appropriate conditions, however, collisions between beam particles and the background gas produce a large number of electrons and ions. These charged particles gradually accumulate in the vicinity of the beam and effectively screen the self-generated electrostatic field of the beam, leading to the establishment of space charge compensation (SCC) and a significant improvement in beam collimation. Notably, the formation of SCC requires a finite time interval, during which the beam still exhibits pronounced divergence before SCC is fully established. Accordingly, a theoretical expression for the build-up time of SCC () is derived, which depends on the background gas density, beam energy, relevant collisional cross sections, and neutralization efficiency. The theoretical predictions show good agreement with the simulation results, validating the accuracy of the model. In addition, the results indicate that when the generation rate of compensating ions is sufficiently high, the system may enter the overcompensation regime, giving rise to periodic oscillations of the space potential. Furthermore, the formation process of SCC and the corresponding beam transport characteristics are systematically analyzed under different background gas pressures and incident beam energies. The beam width decrease at lower beam energies (<1000 keV) and relatively higher background gas pressures, as SCC can be established more effectively under these conditions.